Millions of Volkswagens built over the past 20 years can be broken into with a hack that exploits the cars’ remote control key systems, security researchers have found.

Most VWs built since 1995 use one of a handful of electronic “master keys” to remotely open and lock the doors, and those keys can be extracted by reverse engineering the firmware, the researchers wrote in a new paper.

That alone isn’t enough to break into a car -- the master key has to be combined with a unique code generated by each remote key device. But the researchers also devised a way to do that, assembling a piece of radio hardware costing around $40.

The radio device eavesdrops on the signal sent from the key fob to the car. Once the signals are decrypted, the researchers were able to make copies of the key fob and open the car door.

They tested their method against the VW Jetta, Golf and Passat, as well as the Audi A1, which is also made by Volkswagen.

The researchers, from the University of Birmingham in England and from the German engineering firm Kasper & Oswald, are presenting their paper at the USENIX Security Symposium this week in Austin, Texas.

The researchers notified Volkswagen of their findings last November, and the parties have been having a “constructive exchange,” Volkswagen said. They agreed that the researchers would publish their findings but with no specifics about how they extracted the master keys from the vehicles.

Volkswagen didn't confirm which models were affected but said it would continue to work on its security.

However, the researchers say the vulnerability might not be easy to fix; a costly firmware update would be needed, and that could take time.

It's unknown if criminals have been using the method to break into cars, they noted.

To eavesdrop on the remote control key's radio signal, a bad actor would need to be within 100 meters, which doesn't sound like a big obstacle to overcome.